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O n Temperature Frequency Distribution in the Free Atmosphere
and a Proposed Model for Frontal Analysis
By ROY BERGGREN, University of Uppsalal
(Manuscript received May 1 5
1952)
Abstract
The possibility of tracing baroclinic fields in the lower stratospherc by nieans of temperature
frequency distributions in the main isobaric surfaces is discussed. The existence of a stratospheric
front is indicated by the diagrams.
In the study of thc temperature frequcncy
distribution in the main isobaric surfaces of the
troposphere there is the opportunity to trace
baroclinic fields. Starting with the sloping
baroclinic field connected with frontal layers,
thc iniportancc of which BERGERON
and SWOBODA ointed out already 1924, we may pursue
thc fo lowing reasoning.
Let us begin with the simplest case, that of
thc whole temperature difference between
two air masses being concentrated in the frontal
laycr (see fig. I). If this front is oscillating over a
station, the temperature in a certain isobaric
surface will be constant within the warm air as
well as within the cold air. In the frontal
layer, however, the station will show rapidly
changing temperature. The temperature distribution in an isobaric surface will thercfore
have two maxima, corresponding to the
temperatures of the warm and cold air respectively. The temperatures between these two
maxima will be less frequent. In the real
atmosphere with its baroclinity also outside
f
1 written while on lcave of -absence from Swedish
Meteorological and Hydrological Institute, Stockholm.
Tellus V (Igj3),
I
the frontal layer, the above-mentioned picture
will be less distinctive, but will certainly keep
its main features.
In the case of a sloping large-scale front in
the atmosphere the warmer air is always
situated above the front. This nicans that if a
station has warm air in, say, the 700 mb surface, it must be in the warm air in the 500 mb
surface, too. This gives the same temperature
frequcncies for the two surfaccs. In addition
to thesc cascs, however, we have cold air at
the lower surface and warm air at the upper
surface in all the cases, when the front is
situated between these two isobaric surfaces.
Thus, with increasing height the frequency
of warm air will increase at thc expense of
the frequency of the cold air.
According to MCINTYRE
(1950, p. 102) the
reasoning in the above paragraphs gives thc
necessary and sufficient conditions for the
existence of a sloping baroclinic layer in the
atmosphere. This cannot be quite true, because the case of a horizontal inversion swinging up and down above a station would
give the same characteristic temperature frequency distribution. From an empirical study
ROY BERGGREN
96
mb
I
I.--
mb
100
I.
I50
200
250
3w
400
500
600
mo
800
4y)
HMO
Fig. I . Schematic vertical cross section based on two mean soundings (representative for western Europe and
the eastern part of the middle Atlantic in November). isotherms are given as thin solid (CO,intermediate
valucs are given by dotted lines), isentropes as t h n dashed lines (OK), and frontal boundaries and tropopauses
as heavy lines. The inclination of the front is I/IOO. (After BERGGREN,
1952b, fig. 22.)
of several stations at different latitudes and
their relative frequencies of, say, Tropical
air one can, however, state that the baroclinic
layer must be sloping. From synoptic experience and from theory it is obvious.
The discussion of the temperature distribution in isobaric surfaces can also be applied to
the nearly vertical baroclinic field in the
middle and upper troposphere connected with
the jet stream. This baroclinic field appears
as the strong baroclinity in the warm air immediately above the frontal layer (see e. g.
BERGGREN,
1952 a, fig. 6).
Up to this point a review of the abovementioned paper by MCINTYRE
(19~o)hasbeen
given. When the present author’s attention
was drawn to this paper, he was investigating
some problems connected with the frontal anal-
ysis in the upper troposphere and the lower
stratosphere. In two papers (19~zaand I952b)
I have tried to show that the tropospheric
Polar front in many cases may be prolonged
into the stratosphere. Fig. I in the present
paper gives a schematic vertical cross section
through such a front. If this idea is correct it
ought to be possible to apply McIntyre’s
reasoning to the frequency distributions above
the 300 mb level.
As a first example the British radiosonde
station Lerwick on the Shetland Islands has
been chosen. In order to compare the two
papers, the period used in this study is the
same as that used by McIntyre. From the
Upper Air Section of the Daily Weather Report
of the Meteorological Ofice, London, five winter
months were chosen, viz. January, February,
Tellus V (I953),
I
TEMPERATURE IN THE FREE ATMOSPHERE
020
-
1
0 10
-
150 rnb
-
97
150 mb
1
0.10
,
0 204
0
1
-60"
-70'
020 I
-50'
-
0201
010
-40 C
0-
200 mb
0
-60'
-7b.
,
0 10
-5O'C
0 lo-,
LERW ICK
250 mb
-60'
-5O'C
c
I
I
-Jl-m
I
I
200 mb
- --
1
Tellus V (1g53),
7-205429
I
I
-
I
I
I
1
- 1
ALDERGROVE
0.10
Fig. 2. Winter temperature frequency polygons for
Lerwick (60' N. O I O W). The dashed line gives the
mean values for the different levels.
and December 1947,January and February
1948.Furthermore only the oo GCT or o6GCT
soundings have been used. In McIntyre's
paper it is not clearly pointed out, whether
the investigation is restricted to the night or
early mornirig soundings or not. In our case,
however, we prefer to do so since we are
studying stratospheric conditions, and in that
case the radiation error may cause trouble.
The frequencies in the 700, 500, 400 and
300 mb surfaces are given in McIntyre's paper
as fig. 7. In our fig. z the temperature frequency
distribution of the 250, zoo, 170, and 150 mb
levels are shown. The zso mb distribution
agrees with the 3 0 0 mb distribution given by
McIntyre, who relates the fact that this curve
is near1 Gaussian to the observed fact that at
about t e zso mb level there are almost barotropic conditions along a meridian. In my
papers mentioned above I have pointed out
that the temperatures of the Tropical and
Polar air are about the same at this level.
The fact that the frequency distribution for the
-4O'C
d L-
-
250 mb
-70'
'
I-
170mb
-
m
0,201
-50'
I
I
i
L
-60'
-50'
Fig. 3. Winter temperature frequency polygons for
Aldergrove (ssON, 06OW). The dashed line gives the
mean values for the different levels.
and 300 mb levels shows a marked single maximum, does not imply that we have only one air
mass at this level. The maxima of the two
distributions become so pronounced because
the Polar and Tropical air acquire about the same
temperatures at these levels.
If we continue to the zoo mb level (see fig. 2)
we get the double maxima once more. We
are now well in the stratosphere as far as the
Polar air is concerned but near the tropopause
level in the Tropical air. The ZOO mb surface
is well above the level where the front changes
its character from warm front to cold front
or vice versa (see fig. I).
The Polar air maximum at -54'C
and
the Tropical air maximum at - 6 1 ° C are
easily detectable. If the reasoning in the first
paragraphs is applied to this case, and if the
front model given in fig. I is right, then the
frequency distributions of the 170 mb and
250
98
R O Y BERGGREN
the 130 nib surfaces must show an increase
of the Polar air peak at the expense of the
Tropical air peak. Fig. 2 shows that t h s is
really the case. (A discussion of the reality
of the double maxima will be given below.)
Before going further I must strongly
emphasize that it is not my intention to postulate that this high-tropospheric and lowstratospheric front, seperating tropospheric
Tropical air and stratospheric Polar air, always
can be found. A short discussion of the applicability of the proposed model is given in the
above-mentioned paper (BERGGREN,
1952b).
The frequency diagrams for the British
radiosonde station Aldergrove in northern
Ireland were also constructed. In fact, they
give the same picture as the one from Lerwick,
and they are reproduced as fig. 3 without any
special remark. Especially interesting are the
extreme low temperatures down to -70'
C
or even lower, attained in the Lerwick frequency diagram for 150 mb, but the discussion of this item must be considered outside
the scope of this paper.
In order to be able to compare the results
with those of McIntyre's I have tried to choose
the same period and the same stations as he
did. But unfortunately the North American
radiosonde material for the winter months of
1947 and 1948 were not available here. For
this reason five other winter months have been
chosen. The data from December 1948 and
January 1951 have been taken from Daily
Upper Air Bulletin, the winter months of January, February, and December 1949 from
Daily Series Syrtoptic Wcather Maps.
In fig. 4 the temperature frequency diagrams
for the 700, 500, 300, 200, and 1 3 0 mb surfaces for the radiosonde station Tatoosh Island
in northwestern USA are given.
Before going further we must compare
the mean values for the winter months in
7 0 0 m b - 9.2
joo m b -23.9
3 0 0 m b -47.2
z w m b -56.0
~oomb -
I
I
I
0.10-
-60'
0.10-
I
500 mb
c
-55:
-45'
-50'
-40' C
I
Y
-
I
I
I
-35-
;-25'
-15'C
I
700 m b
-20"
TATOOSh
ISLAND
-10'
Fig. 4. Winter temperature frequency polygons for
Tatoosh Island (48'N. 124'W). The dashed line gives
the mean values for the different levels.
question. These are given in table I. The frequency diagrams given by McIntyre for Tatoosh Island have two maxima in the 700 mb
diagram, corresponding to -2,s'
C and
- 8.6
- 7.2
-10.9
-24.0
-47.5
-55.3
-22.6
-46.8
-53.9
-59.8
-26.6
-48.7
-51.1
-51.9
-
-I
-65'
-21.0
-
I
i-
I
- 5.1
-46.7
-61.3
200 mb
-10.3
-24.9
-48.1
-55.9
I -54.5
-12.0
-12.8
-10.2
-11.9
-26.9
-49.9
-55.0
-52.9
-28.8
-25.4
-47.7
-53.4
-26.6
-50.1
-54.6
-56.0
-49.9
-54.4
-53.3
-
99
TEMPERATURE IN THE FREE ATMOSPHERE
-14,s' C, respectively. As can be seen from
our fig. 4 we have three peaks for the same level,
the warmest of which is situated at -6,s" C.
This discrepancy can be explained if we look
at table I. The winter months chosen by
McIntyre are definitely warmer than the ones
chosen by us. This difference of the mean
temperatures is brought about by the lower
fre uency of warm Tropical air as well as
byxigher frequency of rather cold Polar air.
The other two maxima correspond to old
Polar air and fresh Polar air. The latter of these
two air masses has come down more directly
from the cold air reservoir in the north, being
recently transformed Arctic air.
This lack of warm Tropical air seems to
have almost disappeared at the 500 mb level,
where we get a maximum at -22,s' C, compared with McIn re's at -21,s" C. The higher
frequency of c o d Polar air in our case is
clearly seen in fig. 4, which has an extra
maximum at -36,s" C, whereas McIntyre
has only one cold maximum at -31,s" C.
Anyhow there is no question about the
existence in both cases of a strong baroclinic
field. The warm air maximum in fig. 4 has
increased compared to the distribution at
700 mb at the expense of the cold air maxima.
The single maximum distribution of the
3 0 0 mb surface temperatures is established for
both periods. In our case the temperature
corresponding to maximum frequency is
about 3' C colder than in the other case, and
the distributions have a rather diffetent shape.
If we now continue higher up in the atmosphere, we once more get the three maxima at
the 200 mb level. If there were a sloping
baroclinic field above this station between the
200 and 150 mb surfaces, then the maximum
corresponding to the warm (Polar) air should
increase at the expense of the colder peak.
As can be seen from fig. 4, this is indicated in
the upper diagram. The question whether the
maximum corresponding to Tropical air is
real or not will be discussed below. There a
discussion of the validity of the three maxima
in fig. 4 also will be given.
W e have thus come to the conclusion that
for this North American station as well as
for the British stations there exists a sloping
baroclinic field in the stratosphere.
As to a station situated far to the south on
the North American continent one would
-15'
I
;
-5.C
-5,
-65'C
rl
i?
Tellus V (1953),
7*-2
0 5 42 9
I
Fig. 5 . Winter temperature frequency polygons for
Miami (26"N,80OW). The dashed line gives the mean
values for the different levels.
expect that the sloping baroclinic field seldom
exists. As an example McIntyre has chosen
Santa Maria in California. The fre uency
distribution of this station (see his I g . 2 )
shows a very marked peak corresponding to
Tropical air. The few cases with Polar air
form a tail to the left in the frequency diagram,
more distinct at the 700 nib level than at
500 mb level as is to be expected.
The present author has chosen the station
Miami in Florida (see fig. s), instead of Santa
Maria in southern California. This change
has been done because of the fact that here
the Polar air very seldom reaches above the
700 mb surface and the Tropical air thus
dominates the frequency distribution. The
one-maximum curve must be found at all
levels if the reasoning of the first paragraphs
is right. Fig. 5 gives the frequency distributions
with very marked peaks and the disturbances
come out only as a few lower values in the
700, 500 and 300 mb diagrams. Higher up in
the 200 and IOO mb surfaces these disturbing
values are naturally higher than the teniperature corresponding to the maximum frequency.
I00
R O Y BERGGREN
When studying the temperature frequency
distribution in the main isobaric surfaces for a
single station, it is generally very difficult to
decide whether the different maxima are real
or not. The double maxima of the diagram
for 170 mb in fig. 2 and the triple maxima of
the diagram for 200 mb in fig. 4,for instance,
may be the rcsult of this special sampling.
The populations from which these samples
are drawn might just as well be normally
distributed. When assuming that this is the
case and investigating the deviation of the
sample distributions by standard statistical
methods (X2-methods at the 5 % level) one
obtains no definite results. In some cases the
hypothesis of normal distribution must be
rejected, in others not. Furthermore it may be
so that the population is not normally distributed.
Instead of making a loose assumption about
the distribution and investigating the existence
of a significant deviation the present author
prefers to use an indirect proof. In McIntyre’s
paper as well as in this paper quite a lot of
examples are given and in all cases there are
at least indications of the phenomena on
which the whole reasoning in these papers
are based. The probability that this is a false
result of the ramdom sampling must be
considered small.
My conclusion is thus that the (sloping)
baroclinic field in the troposphere is shown
(and indirectly proved) by McIntyre’s figures,
and the corresponding field in the lower
stratosphere by my figures.
REFERENCES
BERGERON,
T., and SWOBODA,
G., 1924: Wellen und
Wirbel an eincr quasistationaren Grenzflache iiber
Europa. Verid. drs. Geophys. Inrt. drr Uttiu. Leipzig,
111, 2, pp. 63-172.
BERGGREN,
R., 1952a: The Distribution of Temperature
and Wind Connected with Active Tropical Air in
the Higher Troposphere and some Remarks Concerning Clear Air Turbulence at High Altitude. Tellus, 4,
1, pp. 43-53.
BERGGREN,
R., 1952b: O n Frontal Analysis in the Higher
Troposphere and the Lower Stratosphere. Arkiu j ; r
Geqfysik, 2 (in print).
MCINTYRE,
D. P., 1950: O n the Air-Mass Temperature
Distribution in the Middle and N g h Troposphere in
Winter.Joirrnal q/ Mefeor., 7, 2, pp. 101-107.
Sourccs of datk
Climatologicnl Data, U.S. Weather Bureau, Washington.
Daily Series Synoptic Weather Maps, Northern Hemisphere
Sea Level and 500 Millibar Charts with Synoptic
Data Tabulations. U.S. Weather Bureau, Washington.
Daily Upper Air B d l e f i n . U.S. Weather Bureau, Washington.
Daily Weather Report o j the Afetrorological Ofice, Upper
Air Section. Air Ministry, London.
Monthly Wraflirr Review, U.S. Weather Bureau, Washington.
Tellus V (I953),
I